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### Problem:
Mr. Akram invested Rs. 55,000 in shares of two companies, A and B. 

- Company A announced a dividend of 6%.
- Company B announced a dividend of 8%.

The total income received by Mr. Akram from these investments is Rs. 3,900. We need to find the amount he invested in each company, A and B.

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### Solution:

Let:
- \( x \) be the amount invested in Company A.
- \( y \) be the amount invested in Company B.

We have two pieces of information that form our system of equations:

1. **Total Investment**:  
   \[
   x + y = 55000
   \]

2. **Total Income from Dividends**:  
   The income from Company A is \( \frac{6}{100} \times x = 0.06x \),  
   and the income from Company B is \( \frac{8}{100} \times y = 0.08y \).  
   The total income from both companies is Rs. 3,900, so:
   \[
   0.06x + 0.08y = 3900
   \]

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### Solving the Equations

#### Step 1: Express \( y \) in terms of \( x \) from the first equation.

From \( x + y = 55000 \):
\[
y = 55000 - x
\]

#### Step 2: Substitute \( y \) in the second equation.

\[
0.06x + 0.08(55000 - x) = 3900
\]

#### Step 3: Simplify and solve for \( x \).

Expanding the terms:
\[
0.06x + 4400 - 0.08x = 3900
\]

Combine like terms:
\[
-0.02x + 4400 = 3900
\]

Subtract 4400 from both sides:
\[
-0.02x = -500
\]

Divide by -0.02:
\[
x = 25000
\]

#### Step 4: Substitute \( x = 25000 \) back into the first equation to find \( y \).

\[
y = 55000 - 25000 = 30000
\]

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### Answer:
Mr. Akram's investments were:
- Rs. 25,000 in Company A.
- Rs. 30,000 in Company B.

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Would you like a further breakdown of any steps, or have any other questions?

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### Related Questions

1. How would the investments change if the total income were Rs. 4,000?
2. What would be Mr. Akram's income if he invested an equal amount in both companies?
3. How does the dividend percentage affect the income from each company?
4. How would Mr. Akram's total income change if the dividend for Company A increased to 7%?
5. Can you form a general formula to calculate the investment distribution based on different income targets?

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### Tip
When working with percentages in investment problems, setting up equations based on known totals (like total investment and total income) can simplify finding unknown values.

Mr. Akram invested Rs. 55,000 in shares of two companies, A and B. Company A announced a dividend of 6%, and Company B of 8%. If the total income received by Mr. Akram from these investments is Rs. 3,900, what were his investments in Companies A and B?

Solve a real-world investment problem where Mr. Akram invested Rs. 55,000 in two companies, A and B, with dividends of 6% and 8%. Given the total income of Rs. 3,900, learn how to determine his individual investments in each company using systems of linear equations. Suitable for students in Grades 9-10.

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